Subgroups — #16015488

Order 3328.

830 conjugacy classes of subgroups.

The subgroup lattice has 200 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11718519	C₂	1	4	yes	maximal
2	#13123197	C₂	1	2	yes	maximal
3	#13114997	C₂	1	4	yes	maximal
4	#13114995	C₂	1	2	yes	maximal
5	#13114993	C₂	1	1	yes	maximal, characteristic
6	C₄×C₈×Dic₁₃	C₂	1	1	yes	maximal, characteristic
7	C₁₃×#1844	C₂	1	1	yes	maximal, characteristic
8	C₂×#88144	C₂²	1	4	yes	—
9	C₂×C₁₃×#106	C₂²	1	4	yes	—
10	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
11	C₁₃×#384	C₂²	1	2	yes	—
12	C₂×#88057	C₂²	1	4	yes	—
13	C₂×C₈×Dic₁₃	C₂²	1	2	yes	—
14	C₂×C₈×Dic₁₃	C₂²	1	2	yes	—
15	#11718646	—	2	4	no	—
16	#11718638	C₂²	1	4	yes	—
17	#11718634	—	2	4	no	—
18	C₂×#88047	C₂²	1	8	yes	—
19	#11718596	C₂²	1	2	yes	—
20	C₄²×Dic₁₃	C₂²	1	1	yes	characteristic
21	C₂×C₄×#1055	C₂²	1	1	yes	characteristic
22	#11718519	—	2	16	no	—
23	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
24	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
25	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
26	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
27	C₂×C₄⋊Dic₁₃	—	2	4	no	—
28	C₂×C₄⋊Dic₁₃	—	2	4	no	—
29	C₂×C₄⋊Dic₁₃	C₂³	1	4	yes	—
30	C₂×#6101	—	2	4	no	—
31	C₂×C₄×Dic₁₃	D₄	1	4	yes	—
32	C₂×C₄×Dic₁₃	C₂³	1	1	yes	characteristic
33	C₂×C₄×Dic₁₃	C₂³	1	1	yes	characteristic
34	C₂²×#1055	C₂³	1	2	yes	—
35	#88144	—	2	16	no	—
36	C₁₃×#106	—	2	8	no	—
37	C₄×C₈×C₁₃	Q₈	1	4	yes	—
38	#88071	—	2	8	no	—
39	#88057	—	2	8	no	—
40	C₈×Dic₁₃	D₄	1	8	yes	—
41	C₈×Dic₁₃	Q₈	1	8	yes	—
42	#88047	—	2	16	no	—
43	C₄×#1055	Q₈	1	4	yes	—
44	#33311	—	13	1	no	maximal, Sylow
45	C₂²×C₄×C₁₃	—	2	4	no	—
46	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
47	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
48	C₂²×Dic₁₃	—	2	4	no	—
49	C₂²×Dic₁₃	C₂×D₄	1	2	yes	—
50	C₂²×Dic₁₃	C₂×D₄	1	2	yes	—
51	C₂×C₈×C₁₃	C₂×D₄	1	4	yes	—
52	C₂×C₈×C₁₃	C₂×Q₈	1	4	yes	—
53	C₂×C₈×C₁₃	C₂×Q₈	1	4	yes	—
54	C₁₃×C₄⋊C₄	—	2	8	no	—
55	C₁₃×C₄⋊C₄	—	4	8	no	—
56	C₄²×C₁₃	C₂×Q₈	1	2	yes	—
57	C₄²×C₁₃	C₂×Q₈	1	2	yes	—
58	C₄⋊Dic₁₃	—	2	8	no	—
59	C₄⋊Dic₁₃	—	4	8	no	—
60	C₄⋊Dic₁₃	—	4	8	no	—
61	#6101	—	4	8	no	—
62	C₄×Dic₁₃	—	2	8	no	—
63	C₄×Dic₁₃	C₂×D₄	1	4	yes	—
64	C₄×Dic₁₃	C₂×Q₈	1	4	yes	—
65	C₂×#1055	C₂×D₄	1	4	yes	—
66	C₂×#1055	C₂×Q₈	1	4	yes	—
67	C₂×#1055	C₂×Q₈	1	4	yes	—
68	C₂×#499	—	13	4	no	—
69	#2859	—	13	2	no	—
70	#1846	—	13	4	no	—
71	#1845	—	13	2	no	—
72	#1844	—	13	1	no	—
73	#1844	D₁₃	1	1	yes	characteristic
74	C₄²×C₈	—	13	1	no	—
75	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
76	C₂×C₄×C₁₃	—	4	4	no	—
77	C₂×C₄×C₁₃	—	4	8	no	—
78	C₂×C₄×C₁₃	C₄⋊Q₈	1	4	yes	—
79	C₂×C₄×C₁₃	#135	1	8	yes	—
80	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
81	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
82	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
83	C₂×C₄×C₁₃	C₂²×Q₈	1	2	yes	—
84	C₂×Dic₁₃	—	2	4	no	—
85	C₂×Dic₁₃	—	2	4	no	—
86	C₂×Dic₁₃	—	4	4	no	—
87	C₂×Dic₁₃	—	4	8	no	—
88	C₂×Dic₁₃	#127	1	4	yes	—
89	C₂×Dic₁₃	C₄⋊Q₈	1	4	yes	—
90	C₈×C₁₃	C₄⋊Q₈	1	8	yes	—
91	#1055	C₄⋊Q₈	1	8	yes	—
92	C₂×#125	—	13	4	no	—
93	#499	—	26	16	no	—
94	C₂×#107	—	13	8	no	—
95	C₂×#106	—	13	4	no	—
96	C₂×#106	C₂×D₁₃	1	4	yes	—
97	C₂×C₄×C₈	—	13	2	no	—
98	C₂×C₄×C₈	—	13	2	no	—
99	C₂×C₄×C₈	—	13	1	no	—
100	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
101	#389	—	26	4	no	—
102	#389	—	26	4	no	—
103	#384	—	13	2	no	—
104	#384	C₂×D₁₃	1	2	yes	—
105	#382	—	13	4	no	—
106	C₄³	—	13	1	no	—
107	C₂²×C₁₃	C₂×#127	1	1	yes	characteristic
108	C₂²×C₁₃	C₂×C₄⋊Q₈	1	1	yes	characteristic
109	C₂²×C₁₃	C₂×C₄⋊Q₈	1	1	yes	characteristic
110	C₂²×C₁₃	C₂×#135	1	4	yes	—
111	C₄×C₁₃	—	8	4	no	—
112	C₄×C₁₃	#499	1	8	yes	complemented
113	C₄×C₁₃	C₂×C₄⋊Q₈	1	2	yes	—
114	C₄×C₁₃	C₂×C₄⋊Q₈	1	2	yes	—
115	Dic₁₃	—	2	4	no	—
116	Dic₁₃	—	2	4	no	—
117	Dic₁₃	—	8	4	no	—
118	C₂²×C₈	—	13	2	no	—
119	C₂²×C₈	C₂²×D₁₃	1	2	yes	—
120	#125	—	26	16	no	—
121	C₂×C₄⋊C₄	—	2	4	no	—
122	C₂×C₄⋊C₄	—	13	4	no	—
123	C₂×C₄⋊C₄	—	26	4	no	—
124	C₂×C₄⋊C₄	—	26	4	no	—
125	C₂×C₄⋊C₄	—	26	4	no	—
126	C₂×C₄⋊C₄	C₂²×D₁₃	1	4	yes	—
127	C₂×C₄²	—	13	1	no	—
128	C₂×C₄²	—	13	1	no	—
129	C₂×C₄²	—	13	4	no	—
130	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
131	#107	—	26	16	no	—
132	#106	—	2	8	no	—
133	#106	—	26	8	no	—
134	C₄×C₈	—	13	8	no	—
135	C₄×C₈	—	13	8	no	—
136	C₄×C₈	—	13	4	no	—
137	C₄×C₈	Dic₂₆	1	4	yes	—
138	#95	—	26	8	no	—
139	C₂×C₁₃	#2868	1	1	yes	characteristic
140	C₂×C₁₃	#3147	1	2	yes	—
141	C₂×C₁₃	C₂×#499	1	2	yes	—
142	C₂×C₁₃	#3160	1	2	yes	—
143	C₂²×C₄	—	2	4	no	—
144	C₂²×C₄	—	13	2	no	—
145	C₂²×C₄	—	13	2	no	—
146	C₂²×C₄	—	26	4	no	—
147	C₂²×C₄	D₄×D₁₃	1	2	yes	—
148	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
149	C₂×C₈	—	13	4	no	—
150	C₂×C₈	—	13	4	no	—
151	C₂×C₈	—	13	4	no	—
152	C₂×C₈	C₂×Dic₂₆	1	4	yes	—
153	C₂×C₈	D₄×D₁₃	1	4	yes	—
154	C₂×C₈	Q₈×D₁₃	1	4	yes	—
155	C₄⋊C₄	—	2	8	no	—
156	C₄⋊C₄	—	4	8	no	—
157	C₄⋊C₄	—	26	8	no	—
158	C₄⋊C₄	—	52	8	no	—
159	C₄⋊C₄	—	52	8	no	—
160	C₄⋊C₄	—	52	8	no	—
161	C₄²	—	13	4	no	—
162	C₄²	—	13	4	no	—
163	C₄²	—	26	8	no	—
164	C₄²	C₂×Dic₂₆	1	2	yes	—
165	C₄²	Q₈×D₁₃	1	2	yes	—
166	C₁₃	#33311	1	1	yes	characteristic, complemented, Sylow
167	C₂³	C₂×D₄×D₁₃	1	1	yes	characteristic
168	C₂×C₄	—	4	8	no	—
169	C₂×C₄	—	4	4	no	—
170	C₂×C₄	—	13	4	no	—
171	C₂×C₄	—	13	4	no	—
172	C₂×C₄	—	26	4	no	—
173	C₂×C₄	—	26	4	no	—
174	C₂×C₄	—	52	8	no	—
175	C₂×C₄	—	52	4	no	—
176	C₂×C₄	#88142	1	4	yes	—
177	C₂×C₄	#88170	1	8	yes	—
178	C₂×C₄	C₂²×Dic₂₆	1	1	yes	characteristic
179	C₂×C₄	C₂×D₄×D₁₃	1	2	yes	—
180	C₂×C₄	C₂×Q₈×D₁₃	1	1	yes	characteristic
181	C₂×C₄	C₂×Q₈×D₁₃	1	2	yes	—
182	C₈	—	13	8	no	—
183	C₈	#88142	1	8	yes	—
184	C₂²	C₂×#88142	1	1	yes	characteristic
185	C₂²	D₁₃×#127	1	1	yes	characteristic
186	C₂²	D₁₃×C₄⋊Q₈	1	1	yes	characteristic
187	C₂²	C₂×#88170	1	4	yes	—
188	C₄	—	8	4	no	—
189	C₄	—	26	4	no	—
190	C₄	—	26	4	no	—
191	C₄	—	104	4	no	—
192	C₄	#11718519	1	8	yes	complemented
193	C₄	C₂×#88142	1	2	yes	—
194	C₄	D₁₃×C₄⋊Q₈	1	2	yes	—
195	C₂	#13123233	1	1	yes	characteristic
196	C₂	#13125259	1	2	yes	—
197	C₂	C₂×#11718519	1	2	yes	—
198	C₂	#13125345	1	2	yes	—

	subgroup	G/H
center	C₂³	C₂×D₄×D₁₃
commutator, cosocle	C₂²×C₄×C₁₃	C₂⁴
Frattini	C₂²×C₄	C₂³×D₁₃
Fitting	C₁₃×#1844	C₂
socle, prime radical	C₂³×C₁₃	C₂²×D₄
hypercenter	#1844	D₁₃
hypocenter	C₁₃	#33311
LCS	G ▷ C₂²×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1844

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
112. C₄×C₁₃	#499	semidirect
166. C₁₃	#33311	semidirect
192. C₄	#11718519	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×#11718519	2
#13123197	2
#13114997	2
#13114995	2
#13114993	2
C₄×C₈×Dic₁₃	2
C₁₃×#1844	2
#33311	13